Question

The total revenue for Joe’s Realty is given as the function R (X) = 200x-0.5x^2, where X is the number of Bella‘s book. What number of villas book produces the maximum revenue?

Answer 1

To find the maximum revenue, we need to derivate the R(x) function and then solve the equation for x:

$R(x)=200x-0.5x^2$

Derivate the function:

$R^{\prime}(x)=200(1)-2(0.5)x=200-1x$

Then:

$200-x=0$

Therefore:

$x=200$

Which x represents the maximum point, now, replace this value on the R(x) function to find the maximum revenue:

$R(x)=200(200)-0.5(200)^2=20000$